In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenva...In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.展开更多
Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to...Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to B is a nonzero scalar multiple of either a linear＊-isomorphism or a conjugate linear ＊-isomorphism.展开更多
We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those...We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those given in [1] for a simple cycle.We also derive some results for a partial Toeplitz PSD matrix specifying the Cnk pattern to have PSD completion and Toeplitz PSD completion.展开更多
Let R_1 and R_2 be two rings with unit I. We give some characterizations of ring homomorphisms and ring isomorphisms between R_1 and R_2 in term of complete preservers of fixed points of multipliers, under some mild a...Let R_1 and R_2 be two rings with unit I. We give some characterizations of ring homomorphisms and ring isomorphisms between R_1 and R_2 in term of complete preservers of fixed points of multipliers, under some mild assumption on R_1. Applications to several kinds of operator algebras such as Banach algebras, nest algebras, matrix algebras and standard operator algebras are presented.展开更多
In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. Accor...In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given.展开更多
This paper presents an electrical impedance tomography(EIT)method using a partial-differential-equationconstrained optimization approach.The forward problem in the inversion framework is described by a complete electr...This paper presents an electrical impedance tomography(EIT)method using a partial-differential-equationconstrained optimization approach.The forward problem in the inversion framework is described by a complete electrodemodel(CEM),which seeks the electric potential within the domain and at surface electrodes considering the contact impedance between them.The finite element solution of the electric potential has been validated using a commercial code.The inverse medium problem for reconstructing the unknown electrical conductivity profile is formulated as an optimization problem constrained by the CEM.The method seeks the optimal solution of the domain’s electrical conductivity to minimize a Lagrangian functional consisting of a least-squares objective functional and a regularization term.Enforcing the stationarity of the Lagrangian leads to state,adjoint,and control problems,which constitute the Karush-Kuhn-Tucker(KKT)first-order optimality conditions.Subsequently,the electrical conductivity profile of the domain is iteratively updated by solving the KKT conditions in the reduced space of the control variable.Numerical results show that the relative error of the measured and calculated electric potentials after the inversion is less than 1%,demonstrating the successful reconstruction of heterogeneous electrical conductivity profiles using the proposed EIT method.This method thus represents an application framework for nondestructive evaluation of structures and geotechnical site characterization.展开更多
In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. ...In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. in general, a negative answer. Therefore, our question is for what kind of labeled graphs G each partial totally non-positive matrix whose associated graph is G has a totally non-positive completion? If G is not a monotonically labeled graph or monotonically labeled cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion.展开更多
The rapid development of the construction industry has effectively increased the scale of construction engineering and enriched the types of construction projects. In order to promote the development of the constructi...The rapid development of the construction industry has effectively increased the scale of construction engineering and enriched the types of construction projects. In order to promote the development of the construction industry towards a more standardized and professional direction, it is also necessary to do a good job of the overall control of construction costs, in order to improve the overall economic benefits of enterprises. Among them, the most important link is the project completion settlement audit, through the project audit, can intuitively understand the cost information in the process of project construction, fully grasp the dynamic use of funds, to avoid the waste of resources. However, the work of project completion settlement audit is generally more complex, and involves many process links, leading to many problems in the actual work. Therefore, in the follow-up work, we should pay attention to the professionalism and rationality of the project completion settlement audit work, so as to significantly improve the overall level of the construction project completion settlement audit.展开更多
If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t...If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.展开更多
An improved interpolating complex variable element-frees Galerkin(IICVEFG)method for the two-dimensional elastic problems is developed.This method is based on the improved interpolating complex variable moving least-s...An improved interpolating complex variable element-frees Galerkin(IICVEFG)method for the two-dimensional elastic problems is developed.This method is based on the improved interpolating complex variable moving least-squares(IICVMLS)method and the integral form of the elastic problems.In the IICVEFG method,the proposed shape function has the interpolating feature.Therefore,the essential boundary conditions can be exerted directly.Additionally,the unnecessary t erms in the discrete mat rices are removed,which resul ts in a set of concise formulas.This method is verified by analyzing three elastic examples under different constraints and loads.The numerical results show that the IICVEFG method is superior in precision and efficiency to other non-interpolating meshless methods.展开更多
As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optim...As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optimization(DLSO) algorithm is proposed to solve the TSP. Firstly, we introduce discrete coding and order crossover operators in DLSO. Secondly, we use the complete 2-opt(C2-opt) algorithm to enhance the local search ability.Then in order to enhance the efficiency of the algorithm, a parallel discrete lion swarm optimization(PDLSO) algorithm is proposed.The PDLSO has multiple populations, and each sub-population independently runs the DLSO algorithm in parallel. We use the ring topology to transfer information between sub-populations. Experiments on some benchmarks TSP problems show that the DLSO algorithm has a better accuracy than other algorithms, and the PDLSO algorithm can effectively shorten the running time.展开更多
An important aspect of the Orr Sommerfeld problem, which governs the linear stability of parallel shear flows, is concerned with the study of the temporal and spatial spectra for large but finite values of the Reynold...An important aspect of the Orr Sommerfeld problem, which governs the linear stability of parallel shear flows, is concerned with the study of the temporal and spatial spectra for large but finite values of the Reynolds number R . By using only outer (WKB) approximations which are valid in the "complete" sense, we are able to derive approximations to the eigenvalue relation for channel flows, pipe flow, and boundary layer flows which are all remarkably simple and which have a relative error of order ( αR) -1/2 . In this paper, we discuss briefly the basic ideas involved in the derivation of these approximations for boundary layer flows. We then present some results to illustrate the effectiveness of these new approximations. For example, we are even able to compute eigenvalues which lie arbitrarily close to the continuous spectra where all previous numerical treatments have failed.展开更多
In the theory of computational complexity, the travelling salesman problem is a typical one in the NP class. With the aid of a brand-new approach named “maximum-deleting method”, a fast algorithm is constructed for ...In the theory of computational complexity, the travelling salesman problem is a typical one in the NP class. With the aid of a brand-new approach named “maximum-deleting method”, a fast algorithm is constructed for it with a polynomial time of biquadrate, which greatly reduces the computational complexity. Since this problem is also NP-complete, as a corollary, P = NP is proved to be true. It indicates the crack of the well-known open problem named “P versus NP”.展开更多
By using partial order method. some existing theorems of solutions for two-point bouniary value problem of second order ordinary differenlial equations in Banach spaces are given.
In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “...In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “divide” and applied it in construction of solution space. Then, by application of a sticker based parallel algorithm using biological operations, independent set problem was resolved in polynomial time.展开更多
The surface-based DNA computing is one of the methods of DNA computing which uses DNA strands immobilized on a solid surface. In this paper, we applied surface-based DNA computing for solving the dominating set proble...The surface-based DNA computing is one of the methods of DNA computing which uses DNA strands immobilized on a solid surface. In this paper, we applied surface-based DNA computing for solving the dominating set problem. At first step, surface-based DNA solution space was constructed by using appropriate DNA strands. Then, by application of a DNA parallel algorithm, dominating set problem was resolved in polynomial time.展开更多
This works aims to give an answer to the problem P = NP? The result is positive with the criteria that solve the Traveling Salesman Problem in polynomial cost of the input size and a proof is given. This problem gets ...This works aims to give an answer to the problem P = NP? The result is positive with the criteria that solve the Traveling Salesman Problem in polynomial cost of the input size and a proof is given. This problem gets a solution because a polyhedron, with a cut flower looking, is introduced instead of graph (e.g. tree).展开更多
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11061019 and 10962004)the Chunhui Program of Ministry of Education of China (Grant No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia, China(Grant Nos. 2010MS0110 and 2009BS0101)the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University
文摘In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.
基金Supported by the National Natural Science Foundation of China(Grant No.11501401)
文摘Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to B is a nonzero scalar multiple of either a linear＊-isomorphism or a conjugate linear ＊-isomorphism.
基金Research supported in part by National Natural Science Foundation of China No. 10271099. Research supported in part by RGC Grant Nos. 7132/OOP and 7130/02PHKU CRCG Grant Nos 10203501, and 10204437.
文摘We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those given in [1] for a simple cycle.We also derive some results for a partial Toeplitz PSD matrix specifying the Cnk pattern to have PSD completion and Toeplitz PSD completion.
基金Supported by the National Natural Science Foundation of China(Grant No.11671294)
文摘Let R_1 and R_2 be two rings with unit I. We give some characterizations of ring homomorphisms and ring isomorphisms between R_1 and R_2 in term of complete preservers of fixed points of multipliers, under some mild assumption on R_1. Applications to several kinds of operator algebras such as Banach algebras, nest algebras, matrix algebras and standard operator algebras are presented.
文摘In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given.
基金funded by the National Research Foundation of Korea,the Grant from a Basic Science and Engineering Research Project(NRF-2017R1C1B200497515)and the Grant from Basic Laboratory Support Project(NRF-2020R1A4A101882611).
文摘This paper presents an electrical impedance tomography(EIT)method using a partial-differential-equationconstrained optimization approach.The forward problem in the inversion framework is described by a complete electrodemodel(CEM),which seeks the electric potential within the domain and at surface electrodes considering the contact impedance between them.The finite element solution of the electric potential has been validated using a commercial code.The inverse medium problem for reconstructing the unknown electrical conductivity profile is formulated as an optimization problem constrained by the CEM.The method seeks the optimal solution of the domain’s electrical conductivity to minimize a Lagrangian functional consisting of a least-squares objective functional and a regularization term.Enforcing the stationarity of the Lagrangian leads to state,adjoint,and control problems,which constitute the Karush-Kuhn-Tucker(KKT)first-order optimality conditions.Subsequently,the electrical conductivity profile of the domain is iteratively updated by solving the KKT conditions in the reduced space of the control variable.Numerical results show that the relative error of the measured and calculated electric potentials after the inversion is less than 1%,demonstrating the successful reconstruction of heterogeneous electrical conductivity profiles using the proposed EIT method.This method thus represents an application framework for nondestructive evaluation of structures and geotechnical site characterization.
基金The work was supported by the National Science Foundation of China (10571146).
文摘In this paper, the totally non-positive matrix is introduced. The totally non-positive completion asks which partial totally non-positive matrices have a completion to a totally non-positive matrix. This problem has. in general, a negative answer. Therefore, our question is for what kind of labeled graphs G each partial totally non-positive matrix whose associated graph is G has a totally non-positive completion? If G is not a monotonically labeled graph or monotonically labeled cycle, we give necessary and sufficient conditions that guarantee the existence of the desired completion.
文摘The rapid development of the construction industry has effectively increased the scale of construction engineering and enriched the types of construction projects. In order to promote the development of the construction industry towards a more standardized and professional direction, it is also necessary to do a good job of the overall control of construction costs, in order to improve the overall economic benefits of enterprises. Among them, the most important link is the project completion settlement audit, through the project audit, can intuitively understand the cost information in the process of project construction, fully grasp the dynamic use of funds, to avoid the waste of resources. However, the work of project completion settlement audit is generally more complex, and involves many process links, leading to many problems in the actual work. Therefore, in the follow-up work, we should pay attention to the professionalism and rationality of the project completion settlement audit work, so as to significantly improve the overall level of the construction project completion settlement audit.
基金the National Natural Science Foundation of China(No.10674024)
文摘If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.
基金The authors sincerely acknowledge the financial support from the National Science Foundation of China(No.12002240)the National Science and Technology Major Project(No.2017-IV-0003-0040).
文摘An improved interpolating complex variable element-frees Galerkin(IICVEFG)method for the two-dimensional elastic problems is developed.This method is based on the improved interpolating complex variable moving least-squares(IICVMLS)method and the integral form of the elastic problems.In the IICVEFG method,the proposed shape function has the interpolating feature.Therefore,the essential boundary conditions can be exerted directly.Additionally,the unnecessary t erms in the discrete mat rices are removed,which resul ts in a set of concise formulas.This method is verified by analyzing three elastic examples under different constraints and loads.The numerical results show that the IICVEFG method is superior in precision and efficiency to other non-interpolating meshless methods.
基金supported by the National Natural Science Foundation of China(61771293)the Key Project of Shangdong Province(2019JZZY010111)。
文摘As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optimization(DLSO) algorithm is proposed to solve the TSP. Firstly, we introduce discrete coding and order crossover operators in DLSO. Secondly, we use the complete 2-opt(C2-opt) algorithm to enhance the local search ability.Then in order to enhance the efficiency of the algorithm, a parallel discrete lion swarm optimization(PDLSO) algorithm is proposed.The PDLSO has multiple populations, and each sub-population independently runs the DLSO algorithm in parallel. We use the ring topology to transfer information between sub-populations. Experiments on some benchmarks TSP problems show that the DLSO algorithm has a better accuracy than other algorithms, and the PDLSO algorithm can effectively shorten the running time.
文摘An important aspect of the Orr Sommerfeld problem, which governs the linear stability of parallel shear flows, is concerned with the study of the temporal and spatial spectra for large but finite values of the Reynolds number R . By using only outer (WKB) approximations which are valid in the "complete" sense, we are able to derive approximations to the eigenvalue relation for channel flows, pipe flow, and boundary layer flows which are all remarkably simple and which have a relative error of order ( αR) -1/2 . In this paper, we discuss briefly the basic ideas involved in the derivation of these approximations for boundary layer flows. We then present some results to illustrate the effectiveness of these new approximations. For example, we are even able to compute eigenvalues which lie arbitrarily close to the continuous spectra where all previous numerical treatments have failed.
文摘In the theory of computational complexity, the travelling salesman problem is a typical one in the NP class. With the aid of a brand-new approach named “maximum-deleting method”, a fast algorithm is constructed for it with a polynomial time of biquadrate, which greatly reduces the computational complexity. Since this problem is also NP-complete, as a corollary, P = NP is proved to be true. It indicates the crack of the well-known open problem named “P versus NP”.
文摘By using partial order method. some existing theorems of solutions for two-point bouniary value problem of second order ordinary differenlial equations in Banach spaces are given.
文摘In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “divide” and applied it in construction of solution space. Then, by application of a sticker based parallel algorithm using biological operations, independent set problem was resolved in polynomial time.
文摘The surface-based DNA computing is one of the methods of DNA computing which uses DNA strands immobilized on a solid surface. In this paper, we applied surface-based DNA computing for solving the dominating set problem. At first step, surface-based DNA solution space was constructed by using appropriate DNA strands. Then, by application of a DNA parallel algorithm, dominating set problem was resolved in polynomial time.
文摘This works aims to give an answer to the problem P = NP? The result is positive with the criteria that solve the Traveling Salesman Problem in polynomial cost of the input size and a proof is given. This problem gets a solution because a polyhedron, with a cut flower looking, is introduced instead of graph (e.g. tree).
